There is increasingly active work related to Lithium-ion batteries which are widely used for mobile power products, electric vehicles and smart grids. State of charge (SOC) and state of energy (SOE) are key to Lithium-ion battery management. In order to improve accuracy of the battery model, the fractional-order equivalent circuit is used for Lithium-ion battery modeling and its parameters are obtained by genetic algorithm (GA). The developed method for co-estimation of SOC and SOE combines adaptive extended Kalman filter (AEKF) and the recurrent neural network (RNN) with long short-term memory (LSTM) cells. Experiments are set to evaluate the effectiveness of the proposed method under different working conditions. The mean absolute error (MAE) achieved on two working conditions is below 0.5%, indicating the AEKF-LSTM-RNN has excellent capability of achieving accurate and robust battery state estimation.